Cremona's table of elliptic curves

225 = 3² · 5²

Field	Data	Notes
Atkin-Lehner	3+ 5+	Signs for the Atkin-Lehner involutions
Class	225a	Isogeny class
Conductor	225	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-492075 = -1 · 39 · 52	Discriminant
Eigenvalues	0 3+ 5+ -5  0 -5  0 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,0,-34]	[a1,a2,a3,a4,a6]
Generators	[6:13:1]	Generators of the group modulo torsion
j	0	j-invariant
L	1.2453986750529	L(r)(E,1)/r!
Ω	1.350991919679	Real period
R	0.46092010503988	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3600bc2 14400m2 225a1 225b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 225a2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
0	+	+	-5	0	-5	0	-1	0	0	-7	10	0	-5	0	0	0	-13	-5	0	10	-4	0	0	-5

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Quadratic twists for elliptic curve 225a2

-4	8	-3	5	-7	-11	13	17	-19	-23
3600bc2	14400m2	225a1	225b2	11025d2	27225b2	38025g2	65025c2	81225e2	119025b2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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